Have not had much luck with the wiki of late. Tune may be Greek but, I doubt a Greek Mother Riley. Learned this one as Old Mother Riley (had a farm) but the title was:

“Way Down Yonder in the Cornfields
Solo: Old Mother Riley's got a farm,
Chorus: Way down yonder in the cornfields,
S. And on this farm she's got a cow,
C. Way down yonder in the cornfields.
S. Down by the sea,
C. Down by the sea,
S. Where the water melons grow,
C. Where the water melons grow,
S. Back to ma home,
C. Back to ma home,
S. I dare not go––
C. I dare not go,
S. For if I do––
C. For if I do,
S. My Ma will say––
C. My Ma will say:
S. Have you ever seen a cow with a green eyebrow?
C. Have you ever seen a cow with a green eyebrow?
C. Down by the E.I.O.”
[More Tommy's Tunes, 2nd series, Nettleinghame, 1918]
Note: With music.

fwiw: Right about the time Arthur Lucan (1885-1934) got married and created his Old Mother Riley stage character.